Pat dry beef cubes with paper towel and sprinkle them with salt and pepper.
Heat the oil in a large Dutch oven or heavy based pot. Sauté the pancetta over medium heat for about 3 – 5 minutes, until crisp and browned. Transfer with a slotted spoon to a plate and set aside.
In batches, sear the beef in the hot oil until browned on all sides. Remove to the plate with the pancetta.
In the remaining oil, sauté the carrots and onions until softened, (about 3 minutes), then add the minced garlic and cook for 30 seconds. Return the pancetta and beef back into the pot.
Add the wine and enough beef stock so that the meat is covered. Then add the tomato paste, thyme, and bay leaves. Bring to a boil.
Cover, transfer to the oven and simmer for 1 1/2 hours. Add pearl onions and return to oven for an additional 2 – 2 ½ hours.
Thirty minutes before the stew is done, heat 2 tablespoons of butter in a medium-sized skillet. Add the mushrooms and sauté for about 10 minutes until lightly browned. Remove from heat.
Meanwhile, combine 2 tablespoons of butter and the flour with a fork making sure they are well combined.
Remove the stew from the oven. Remove the bay leaves and thyme sprigs, and stir in the butter/flour mixture. Add the mushrooms and return to the oven for 15 minutes.
Remove from the oven and sprinkle chopped parsley over the top. It’s good by itself, or serve with mashed potatoes, rice, or noodles.